A novel approach to the characteristic splitting scheme for mildly compressible flows based on the weighted averaged flux method

Abstract

In the present work we improve the characteristic splitting approach for computing mildly compressible flows. This splitting approach is consisted of two separate steps namely an advective step and a purely hyperbolic, acoustic step. Typically, a pressure correction method is used for solving the acoustic step which may lead to overly dispersive, incorrect results. As a remedy to this issue, a novel solution approach on the basis of the weighted averaged flux method (WAF) is proposed, which solves the non-conservative, hyperbolic equations of the acoustic step directly. The stability and accuracy of this novel WAF method is demonstrated and an implicit, monotone formulation for three-dimensional unstructured grids is given. The simulation of the non-reacting flow in a swirl burner proves the applicability of the method.